What do you mean by hacked? I am sure I asked this on another thread but got no answer. Why would a 'hacked' router slow down, and why do you think this is this common?
A compromised router would appear to slow down because the upstream bandwidth is being used for nefarious activities. Might be as simple as a distributed denial of service on some target. It could be a hacker using the router to go after a high value target; if you want to hack the Pentagon first compromise someone else's router and go from there. Then the police come knocking on someone else's door. Alternatively they could just be using your router as a proxy for illegal content - anything form movie downloads to child pornography. Again the police are going to come knocking on someone else's door rather than theirs. If they wipe the logs of the router when they are finished it then becomes very very hard to trace. For extra safety string a few compromised routers together.
I think it is common because there are millions of devices out there not getting security updates. If you have not had a security update in a couple of years then it is almost certain there are vulnerabilities in your device.
There is a possibility that badly written software could over time consume more and more resources on the device. However if the manufacturer can't fix that then they are unlikely to be able to fix security vulnerabilities, and the device is junk anyway and you are best getting replacing it with something that does not need restarting every few days or more frequent.
In my personal experience that has not been the case however. The routers where being compromised repeatedly even though they where not on static IP addresses. I do accept that the vast majority of people would be unable to make this determination though as they would lack the skill set required.
Basically all you need to do is read through the CERT vulnerabilities list for the last few years, pick one and test it against the router model of your choice. Then head over to Shodan and do a quick search and start compromising devices
I would add that consumer grade routers tend to be a low priority for security researchers because few if any vendors offer bug bounties. Heck most of them won't even acknowledge there is a problem with their firmware let alone issue an update. That said from time to time you will see long lists of router models with vulnerabilities that never get addressed by the vendors.